Additive multipliers

[Thalassicus]

Do two 50% penalties add or multiply?

In other words, additive to the defender's value in X * (bonuses) / (penalties) like cIV's insanely complicated combat formulas and % calculations after relative strength is determined... or just simple multipliers like most games? I haven't seen much info on combat formulas. If anyone can point me in the direction of a reference it'd be appreciated. Some searches through the currently posted guides and forum searches haven't been successful in coming up with info.

A: * (1 + sum of bonuses) / (1 + sum of penalties)
B: * (product of bonuses) * (product of penalties)

 

[Casta]

Im not sure myself, but I can confirm one thing.

Forbidden palace and the same bonus in the order policy tree stacks to a 100% reducement of unhappiness from number of cities, ie. completely negating that factor. (which imo is pretty damn sick)

 

[Unearthly]

Most things are additive, but not everything. For example I found that as Ghandi, Theocracy reduced my modified happiness rather than my base happiness. So this was a multiplicative modifier. However, as Casta states, modifiers to unhappiness from cities is additive. This is great for everyone but Ghandi.

I haven't tested which is the case for combat, but I'll try firing the game up and seeing which it is.

-EDIT- Ok, it's definitely additive. There is a Longsword who has +45% flanking bonus, but -33% terrain bonus. Using additive modifiers the strength comes to exactly what's printed in game.

18*(1+.45-.33) = 20.16

 

[tokala]

Combat boni seem to be additive. I wondered how it could happen that a full health sword was insta-killed by a 10 city, thought it to be a bug at first glance.
When the next one approached, I had a chariot ready and the mouseover showed an adjusted strength of ~2 for the sword . Open ground+pillaged iron=OUCH.

 

[pi-r8]

Everything's additive. Bonuses add together with penalties, and can cancel them out. For example if you have great general + Himeji castle (total 50% bonus) and the lack of resource penalty (-50% bonus) then your strenght is unchanged.

This means your strength can drop really, really fast if you stack penalties. One time I tried to attack a city with a GDR while I was lacking uranium. -50% resource penalty, -40% city attack penalty meant that it was fighting at only 10% of its strength. A strength 15 attack lol.

edit: now i'm curious to see what happens when you attack an unpromoted lancer on flat land while they're lacking horses. (total -133% penalty) Do they defend at negative strength?

 

[Thalassicus]

@Unearthly, tokala
Bonuses are additive, the question is how penalties are handled though. Bonuses and penalties are very different. Like pi-r8 points out, additive penalties can get weird situations. You can have a +1000% bonus and things still make sense (10/1), but with a -100% penalty (or more) things don't make sense (1/0 indeterminate divide-by-zero).

An even more likely situation would be attacking with fighters low on oil, since they start without experience, and would be negative strength (-75% -50%). If strength represents damage the unit can deal, negative strength would mean the unit should deal negative damage, ie heal the enemy. Fighters dropping gift baskets and free ammo!

Civ IV worked around this by reversing the penalty and adding it as a bonus to the defender (and most games have multipliers multiply instead of add)... but if Civ V lets penalties stack and strength can go negative...

I guess there's one way to find out for sure, I'll create a test map and see what happens. I'm surprised this hasn't been done yet! It's a rather basic and fundamental part of the game, especially since open terrain gives a universal penalty.


Update: Well, with a lancer at -166% I can confirm it doesn't use exactly the same system as CiV's bonuses or cIV's method. Civ IV would divide base strength by 2.66, resulting in 8 not 2, and just adding everything up directly would result in -14. It might ignore penalties past -90%, I'm doing further testing.

 

[tokala]

Might get capped at 10%. Isn't the lancer base strength 22?

 

[Thalassicus]

Yep, can confirm that now after testing other units. The way penalties work means there's also some rather counter-intuitive aspects to gameplay...

Shock actually gives +31% defending in the open, while Drill gives +16% defending on rough. Shock is twice as powerful despite both stating 20%, due to the bizzare method of directly additive penalties, unlike Civ IV or other games.

 

[neptune2000]

Yep, can confirm that now after testing other units. The way penalties work means there's also some rather counter-intuitive aspects to gameplay...

Shock actually gives +31% defending in the open, while Drill gives +16% defending on rough. Shock is twice as powerful despite both stating 20%, due to the bizzare method of directly additive penalties, unlike Civ IV or other games.

Thanks for testing all this. I'm a bit confused however. 2 things. Are you confirming the -90% minimum posited above? And also, can you explain how you got to the +31% / +16% numbers for Shock and Drill?

 

[Nunya]

Defending in the open normally gives a 33% penalty so you fight at 67% strength. with Shock I you fight at 87% strength. 87 is 130% of 67 so you fight 30% better. Meanwhile in rough terrain you normally defend at 125% and with Drill I you defend at 145%. 145 is 116% of 125 so you fight 16% better.

 

[Thalassicus]

Here's an easy way to think about it. 50% -> 100% doubles, but 100% -> 150% only increases by half (even though both added 50%). I can confirm the -90% minimum penalty, anything beyond that is simply ignored.

If the multipliers were multiplied (like most other games) instead of added, promotions wouldn't have this odd behavior. (Multiplying gives the same effect no matter what the starting value was.)

Basically, just remember that promotions counteracting a penalty have a much bigger effect than situations without a penalty.